# Towards Complex Dynamic Physics System Simulation with Graph Neural ODEs

arXiv: https://arxiv.org/abs/2305.12334 · HTML: https://mlsanity.com/paper/2305.12334/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 60 references that are in the map.
- First posted on arXiv 21 May 2023.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2103.00113/) (2021)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Transformers for Modeling Physical Systems](https://mlsanity.com/paper/2010.03957/) (2020)
- [Network Representation Learning: A Survey](https://mlsanity.com/paper/1801.05852/) (2017)

## Built on by (most cited first, 8 of 8)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [HOP: Heterogeneous Topology-based Multimodal Entanglement for Co-Speech Gesture Generation](https://mlsanity.com/paper/2503.01175/) (2025)
- [ControlSynth Neural ODEs: Modeling Dynamical Systems with Guaranteed Convergence](https://mlsanity.com/paper/2411.02292/) (2024)
- [DEL: Discrete Element Learner for Learning 3D Particle Dynamics with Neural Rendering](https://mlsanity.com/paper/2410.08983/) (2024)
- [Graph Neural Stochastic Differential Equations](https://mlsanity.com/paper/2308.12316/) (2023)
- [ICODE: Modeling Dynamical Systems with Extrinsic Input Information](https://mlsanity.com/paper/2411.13914/) (2024)
- [PointODE: Lightweight Point Cloud Learning with Neural Ordinary Differential Equations on Edge](https://mlsanity.com/paper/2506.00438/) (2025)

## Abstract (arXiv)

The great learning ability of deep learning models facilitates us to comprehend the real physical world, making learning to simulate complicated particle systems a promising endeavour. However, the complex laws of the physical world pose significant challenges to the learning based simulations, such as the varying spatial dependencies between interacting particles and varying temporal dependencies between particle system states in different time stamps, which dominate particles' interacting behaviour and the physical systems' evolution patterns. Existing learning based simulation methods fail to fully account for the complexities, making them unable to yield satisfactory simulations. To better comprehend the complex physical laws, this paper proposes a novel learning based simulation model- Graph Networks with Spatial-Temporal neural Ordinary Equations (GNSTODE)- that characterizes the varying spatial and temporal dependencies in particle systems using a united end-to-end framework. Through training with real-world particle-particle interaction observations, GNSTODE is able to simulate any possible particle systems with high precisions. We empirically evaluate GNSTODE's simulation performance on two real-world particle systems, Gravity and Coulomb, with varying levels of spatial and temporal dependencies. The results show that the proposed GNSTODE yields significantly better simulations than state-of-the-art learning based simulation methods, which proves that GNSTODE can serve as an effective solution to particle simulations in real-world application.